`Learning.detAlgorithm`🔗

This page has the declaration's own card below, then its dependency graph, then a card for each dependency (type dependencies first, then the rest of the transitive closure). For a theorem, the graph and the dependency cards only follow its statement's dependencies (its proof is replaced by sorry, so what it proves doesn't depend on how); for everything else, both the type and the body/value are followed, since their content is part of what later declarations build on.

Minimal Lean file

`detAlgorithm`🔗

DefinitionLearning.detAlgorithm

Details

A deterministic algorithm, which chooses the action given by the function nextAction.

def

Learning.detAlgorithm.{u_1, u_2} {𝓐 : Type u_1} {𝓨 : Type u_2}
  {m𝓐 : MeasurableSpace 𝓐} {m𝓨 : MeasurableSpace 𝓨}
  (nextA : (n : ℕ) → (↥(Finset.Iic n) → 𝓐 × 𝓨) → 𝓐)
  (h_next : ∀ (n : ℕ), Measurable (nextA n)) (action0 : 𝓐) :
  Algorithm 𝓐 𝓨
Learning.detAlgorithm.{u_1, u_2}
  {𝓐 : Type u_1} {𝓨 : Type u_2}
  {m𝓐 : MeasurableSpace 𝓐}
  {m𝓨 : MeasurableSpace 𝓨}
  (nextA :
    (n : ℕ) →
      (↥(Finset.Iic n) → 𝓐 × 𝓨) → 𝓐)
  (h_next :
    ∀ (n : ℕ), Measurable (nextA n))
  (action0 : 𝓐) : Algorithm 𝓐 𝓨

Code

noncomputable
def detAlgorithm (nextA : (n : ℕ) → (Iic n → 𝓐 × 𝓨) → 𝓐)
    (h_next : ∀ n, Measurable (nextA n)) (action0 : 𝓐) :
    Algorithm 𝓐 𝓨 where
  policy n := Kernel.deterministic (nextA n) (h_next n)
  p0 := Measure.dirac action0

Type uses (1)

Algorithm

Used by (15)

Actions: Source · Open Issue

Dependency graph

Type dependencies (1)

`Algorithm`🔗

StructureLearning.Algorithm

Details

A stochastic, sequential algorithm.

structure

Learning.Algorithm.{u_4, u_5} (𝓐 : Type u_4) (𝓨 : Type u_5)
  [MeasurableSpace 𝓐] [MeasurableSpace 𝓨] : Type (max u_4 u_5)
Learning.Algorithm.{u_4, u_5}
  (𝓐 : Type u_4) (𝓨 : Type u_5)
  [MeasurableSpace 𝓐]
  [MeasurableSpace 𝓨] : Type (max u_4 u_5)

Code

structure Algorithm (𝓐 𝓨 : Type*) [MeasurableSpace 𝓐] [MeasurableSpace 𝓨] where
  /-- Policy or sampling rule: distribution of the next action. -/
  policy : (n : ℕ) → Kernel (Iic n → 𝓐 × 𝓨) 𝓐
  /-- The policy is a Markov kernel. -/
  [h_policy : ∀ n, IsMarkovKernel (policy n)]
  /-- Distribution of the first action. -/
  p0 : Measure 𝓐
  /-- The first action distribution is a probability measure. -/
  [hp0 : IsProbabilityMeasure p0]

Used by (216)

Actions: Source · Open Issue

Learning.detAlgorithm🔗

detAlgorithm🔗

Algorithm🔗

`Learning.detAlgorithm`🔗

`detAlgorithm`🔗

`Algorithm`🔗